In the following tables, `\({\tau }_{pre}\) ', `\(C_{pre}\) ', `\(B_{pre}\) ' and `\(N_{pre}\) ' represent the PCG method with the \(\tau \) -preconditioner, the Strang circulant preconditioner, the banded preconditioner, and no preconditioner, respectively. `\(M_{pre}\) ' denotes the multigrid preconditioned method with the banded preconditioner proposed in [1]} and `\(MGM\) ' represents the algebraic multigrid method shown in [2]}.
Besides, `\(n\) ' denotes the spatial grid points, `Iter' displays the number of iterations required for convergence by those methods, and `CPU(s)' signifies the CPU time in second for solving the linear systems. In particular, `\(-\) ' implies the CPU time over \(10^4\)  and `\(*\) ' represents the number of iterations over \(10^3\) .
For all tested methods, let \(u_{0}=0\)  be the initial guess and the stopping criterion is chosen as
\(\frac{\left\Vert r_{q}\right\Vert _2}{\left\Vert r_{0}\right\Vert _2}<10^{-8},\) 
